"The "deliberate lie" was that Britain supplied small arms ammunition to Syria - " the sale was documented,"

That is news Christmas, could you perhaps share with us where this sale is documented?

A newspaper article referring to the granting of an export licence is documentary proof of nothing. The issuing of a licence is not a guarantee that any sale or purchase ever occurred. All it means is that whoever applied for the licence (and that was not the British Government) could enter into negotiations and pursue the deal. Nobody is going to waste time and money talking to you about buying anything unless they are sure that you can deliver.

The process is licences, paperwork and permits first and that Christmas would be before the person we are talking about here (note person, private individual, not Government body) even bought the ammunition referred to in your newspaper article, otherwise the would be seller is left with something he cannot sell on. Arms dealers may be many things - being Stupid is not something you can accuse them of being.